Change Detection in Complex Dynamical Systems Using Intrinsic Phase and Amplitude Synchronization

Abstract

We present an approach for the detection of sharp change points (short-lived and persistent) in nonlinear and nonstationary dynamic systems under high levels of noise by tracking the local phase and amplitude synchronization among the components of a univariate time series signal. The signal components are derived via Intrinsic Time scale Decomposition (ITD)–a nonlinear, non-parametric analysis method. We show that the signatures of sharp change points are retained across multiple ITD components with a significantly higher probability as compared to random signal fluctuations. Theoretical results are presented to show that combining the change point information retained across a specific set of ITD components offers the possibility of detecting sharp transitions with high specificity and sensitivity. Subsequently, we introduce a concept of mutual agreement to identify the set of ITD components that are most likely to capture the information about dynamical changes of interest and define an InSync statistic to capture this local information. Extensive numerical, as well as real-world case studies involving benchmark neurophysiological processes and industrial machine sensor data, suggest that the present method can detect sharp change points, on an average 62% earlier (in terms of average run length) as compared to other contemporary methods tested.